X-ray absorption fine structure XAFS is a powerful technique for probing the local environment of metal atoms in biological macromolecules. These metal atoms are common in the active sites of enzymes, for example, and are essential for their function. Analysis of XAFS data is a time consuming activity that requires extensive experience to do correctly, limiting the range of applicability of the technique. In an attempt to improve this situation, we have applied the approach of Tikhonov regularization to solve the inverse problem of reconstructing the distribution of atoms directly, without resorting to ad-hoc assumptions about its shape. The procedure has performed excellently in test cases, resolving features that are normally unresolvable, and since the method is linear, there is no difficulty with local minima. The regularization procedure can be done on ordinary desktop computers in minutes, and we have satisfactorily reconstructed the distributions for several atomic types simultaneously. In test cases we have found the method far outperforms traditional approaches. We are presently working to generalize this method for multiple scattering. This work represents a promising development towards direct methods which can be expected to yield more reliable results and interpretations in future studies.